29 September 2017
Maximum Entropy
Maximum Entropy
Maximum Entropy
Maximum Entropy
Maximum Entropy
Maximum Entropy
Maximum Entropy and Macroecology
The core of METE
Ecosystem structure function (ESF) \[ R(n, \varepsilon \mid S_0, N_0, E_0) = \text{joint prob of abundance and metab rate} \] Species abundance and metabolic rate distributions follow
Spatial structure function (SSF) \[ \Pi(n_i \mid N_0, n_0, A_0, A) = \text{prob of abundance in cell of size } A \] Spatial abundance distribution and species area relationship follow
meteR
meteR: Data + Core
library(meteR) data(arth) head(arth)
## spp count mass ## 1 blacchel 1 4.7480 ## 2 mecyocul 1 1.6490 ## 3 eurynsp1 1 0.2584 ## 4 eurynsp1 1 0.2584 ## 5 eurynsp1 1 0.2584 ## 6 eurynsp1 1 0.2584
arthESF <- meteESF(spp = arth$spp, abund = arth$count,
power = arth$mass^0.75)
arthESF # this is the print method
## METE object with state variables: ## S0 N0 E0 ## 76.00 547.00 15868.26 ## ## with Lagrange multipliers: ## la1 la2 ## 0.037929267 0.004960427
meteR: Data + Core
length(unique(arth$spp))
## [1] 76
sum(arth$count)
## [1] 547
sum(arth$mass^0.75 / min(arth$mass^0.75))
## [1] 15868.26
arthESF_stateVar <- meteESF(S0 = 76, N0 = 547, E0 = 15868.26)
meteR: Data + Core
data(anbo) head(anbo)
## row column spp count ## 1 3 3 cabr 3 ## 2 3 3 caspi1 20 ## 3 3 3 crcr 3 ## 4 3 3 crsp2 1 ## 5 3 3 gnwe 11 ## 6 3 3 grass 11
anboSSF <- meteSSF(spp = anbo$spp, sppID = 'gnwe',
abund = anbo$count, row = anbo$row,
col = anbo$column, A = 1, A0 = 16)
anboSSF
## METE object with state variables: ## n0 A A0 ## 41 1 16 ## ## with Lagrange multipliers: ## [1] 0.3294792
meteR: Prediction + Analysis
arthSAD <- sad(arthESF) plot(arthSAD, ptype = 'rad')
logLik(arthSAD)
## 'log Lik.' -201.8189 (df=2)
meteR: Prediction + Analysis
anboSAR <- meteSAR(spp = anbo$spp, abund = anbo$count,
row = anbo$row, col = anbo$col,
Amin = 1, A0 = 16)
plot(anboSAR)
mse(anboSAR)
## [1] 29.79903